<p>Mutual illumination occurs when light reflected from one surface impinges on a second one. The resulting additional illumination incident on the second surface affects both the color and intensity of the light reflected from it. As a consequence, the image of a surface in the presence of mutual illumination differs from what it otherwise would have been in the absence of mutual illumination. Unaccounted for mutual illumination can easily confuse methods that rely on intensity or color such as shape-from-shading or color-based object recognition. In this correspondence, we introduce an algorithm that removes mutual illumination effects from images. The domain is that of previously-segmented images of convex surfaces of uniform color and diffuse reflectance where for each surface the interreflection occurs mainly from one other surface and can be accurately accounted for within a one-bounce model. The algorithm is based on a singular value decomposition of the colors coming from each surface. Geometrical information about where on the surface the colors emanate from is not required. The RGB triples from a single convex surface experiencing interreflection fall in a plane; intersecting the planes generated from two interreflecting surfaces results in a unique interreflection color. Each pixel can then be factored into its interreflection and no-interreflection components so that a complete no-interreflection image is produced.</p>